LMFDB - Embedded newform 3549.2.a.bh.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.49813$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.49813 q^{2} +1.00000 q^{3} +4.24068 q^{4} +2.35199 q^{5} +2.49813 q^{6} -1.00000 q^{7} +5.59751 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.49813 q^{2} +1.00000 q^{3} +4.24068 q^{4} +2.35199 q^{5} +2.49813 q^{6} -1.00000 q^{7} +5.59751 q^{8} +1.00000 q^{9} +5.87558 q^{10} +5.16537 q^{11} +4.24068 q^{12} -2.49813 q^{14} +2.35199 q^{15} +5.50198 q^{16} -1.70559 q^{17} +2.49813 q^{18} -8.02484 q^{19} +9.97401 q^{20} -1.00000 q^{21} +12.9038 q^{22} +4.21818 q^{23} +5.59751 q^{24} +0.531841 q^{25} +1.00000 q^{27} -4.24068 q^{28} -5.24033 q^{29} +5.87558 q^{30} +1.11538 q^{31} +2.54966 q^{32} +5.16537 q^{33} -4.26078 q^{34} -2.35199 q^{35} +4.24068 q^{36} +8.21263 q^{37} -20.0471 q^{38} +13.1653 q^{40} -6.75466 q^{41} -2.49813 q^{42} -0.965145 q^{43} +21.9047 q^{44} +2.35199 q^{45} +10.5376 q^{46} +9.18662 q^{47} +5.50198 q^{48} +1.00000 q^{49} +1.32861 q^{50} -1.70559 q^{51} +11.9257 q^{53} +2.49813 q^{54} +12.1489 q^{55} -5.59751 q^{56} -8.02484 q^{57} -13.0910 q^{58} -2.98003 q^{59} +9.97401 q^{60} -14.6034 q^{61} +2.78637 q^{62} -1.00000 q^{63} -4.63456 q^{64} +12.9038 q^{66} -13.5464 q^{67} -7.23283 q^{68} +4.21818 q^{69} -5.87558 q^{70} +0.318196 q^{71} +5.59751 q^{72} -0.542709 q^{73} +20.5162 q^{74} +0.531841 q^{75} -34.0307 q^{76} -5.16537 q^{77} -13.2301 q^{79} +12.9406 q^{80} +1.00000 q^{81} -16.8740 q^{82} +5.79295 q^{83} -4.24068 q^{84} -4.01151 q^{85} -2.41106 q^{86} -5.24033 q^{87} +28.9132 q^{88} -7.80950 q^{89} +5.87558 q^{90} +17.8879 q^{92} +1.11538 q^{93} +22.9494 q^{94} -18.8743 q^{95} +2.54966 q^{96} -0.287042 q^{97} +2.49813 q^{98} +5.16537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.49813	1.76645	0.883224	−	0.468952i	$-0.155368\pi$
$2$	2.49813	1.76645	0.883224	+	0.468952i	$0.155368\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.24068	2.12034
$5$	2.35199	1.05184	0.525920	−	0.850534i	$-0.323721\pi$
$5$	2.35199	1.05184	0.525920	+	0.850534i	$0.323721\pi$
$6$	2.49813	1.01986
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	5.59751	1.97902
$9$	1.00000	0.333333
$10$	5.87558	1.85802
$11$	5.16537	1.55742	0.778709	−	0.627385i	$-0.215875\pi$
$11$	5.16537	1.55742	0.778709	+	0.627385i	$0.215875\pi$
$12$	4.24068	1.22418
$13$	0	0
$13$	0	0
$14$	−2.49813	−0.667654
$15$	2.35199	0.607280
$16$	5.50198	1.37549
$17$	−1.70559	−0.413665	−0.206833	−	0.978376i	$-0.566316\pi$
$17$	−1.70559	−0.413665	−0.206833	+	0.978376i	$0.566316\pi$
$18$	2.49813	0.588816
$19$	−8.02484	−1.84102	−0.920512	−	0.390715i	$-0.872228\pi$
$19$	−8.02484	−1.84102	−0.920512	+	0.390715i	$0.872228\pi$
$20$	9.97401	2.23026
$21$	−1.00000	−0.218218
$22$	12.9038	2.75110
$23$	4.21818	0.879552	0.439776	−	0.898108i	$-0.355058\pi$
$23$	4.21818	0.879552	0.439776	+	0.898108i	$0.355058\pi$
$24$	5.59751	1.14259
$25$	0.531841	0.106368
$26$	0	0
$27$	1.00000	0.192450
$28$	−4.24068	−0.801412
$29$	−5.24033	−0.973104	−0.486552	−	0.873652i	$-0.661746\pi$
$29$	−5.24033	−0.973104	−0.486552	+	0.873652i	$0.661746\pi$
$30$	5.87558	1.07273
$31$	1.11538	0.200328	0.100164	−	0.994971i	$-0.468063\pi$
$31$	1.11538	0.200328	0.100164	+	0.994971i	$0.468063\pi$
$32$	2.54966	0.450720
$33$	5.16537	0.899176
$34$	−4.26078	−0.730718
$35$	−2.35199	−0.397558
$36$	4.24068	0.706779
$37$	8.21263	1.35015	0.675074	−	0.737750i	$-0.264112\pi$
$37$	8.21263	1.35015	0.675074	+	0.737750i	$0.264112\pi$
$38$	−20.0471	−3.25207
$39$	0	0
$40$	13.1653	2.08161
$41$	−6.75466	−1.05490	−0.527450	−	0.849586i	$-0.676852\pi$
$41$	−6.75466	−1.05490	−0.527450	+	0.849586i	$0.676852\pi$
$42$	−2.49813	−0.385470
$43$	−0.965145	−0.147183	−0.0735916	−	0.997288i	$-0.523446\pi$
$43$	−0.965145	−0.147183	−0.0735916	+	0.997288i	$0.523446\pi$
$44$	21.9047	3.30225
$45$	2.35199	0.350613
$46$	10.5376	1.55368
$47$	9.18662	1.34001	0.670003	−	0.742358i	$-0.266293\pi$
$47$	9.18662	1.34001	0.670003	+	0.742358i	$0.266293\pi$
$48$	5.50198	0.794142
$49$	1.00000	0.142857
$50$	1.32861	0.187894
$51$	−1.70559	−0.238830
$52$	0	0
$53$	11.9257	1.63812	0.819059	−	0.573709i	$-0.194496\pi$
$53$	11.9257	1.63812	0.819059	+	0.573709i	$0.194496\pi$
$54$	2.49813	0.339953
$55$	12.1489	1.63816
$56$	−5.59751	−0.747998
$57$	−8.02484	−1.06292
$58$	−13.0910	−1.71894
$59$	−2.98003	−0.387966	−0.193983	−	0.981005i	$-0.562141\pi$
$59$	−2.98003	−0.387966	−0.193983	+	0.981005i	$0.562141\pi$
$60$	9.97401	1.28764
$61$	−14.6034	−1.86977	−0.934884	−	0.354954i	$-0.884497\pi$
$61$	−14.6034	−1.86977	−0.934884	+	0.354954i	$0.884497\pi$
$62$	2.78637	0.353869
$63$	−1.00000	−0.125988
$64$	−4.63456	−0.579320
$65$	0	0
$66$	12.9038	1.58835
$67$	−13.5464	−1.65496	−0.827478	−	0.561499i	$-0.810225\pi$
$67$	−13.5464	−1.65496	−0.827478	+	0.561499i	$0.810225\pi$
$68$	−7.23283	−0.877110
$69$	4.21818	0.507809
$70$	−5.87558	−0.702266
$71$	0.318196	0.0377629	0.0188814	−	0.999822i	$-0.493989\pi$
$71$	0.318196	0.0377629	0.0188814	+	0.999822i	$0.493989\pi$
$72$	5.59751	0.659673
$73$	−0.542709	−0.0635193	−0.0317596	−	0.999496i	$-0.510111\pi$
$73$	−0.542709	−0.0635193	−0.0317596	+	0.999496i	$0.510111\pi$
$74$	20.5162	2.38496
$75$	0.531841	0.0614117
$76$	−34.0307	−3.90359
$77$	−5.16537	−0.588649
$78$	0	0
$79$	−13.2301	−1.48850	−0.744249	−	0.667903i	$-0.767192\pi$
$79$	−13.2301	−1.48850	−0.744249	+	0.667903i	$0.767192\pi$
$80$	12.9406	1.44680
$81$	1.00000	0.111111
$82$	−16.8740	−1.86343
$83$	5.79295	0.635859	0.317930	−	0.948114i	$-0.397012\pi$
$83$	5.79295	0.635859	0.317930	+	0.948114i	$0.397012\pi$
$84$	−4.24068	−0.462696
$85$	−4.01151	−0.435110
$86$	−2.41106	−0.259991
$87$	−5.24033	−0.561822
$88$	28.9132	3.08216
$89$	−7.80950	−0.827805	−0.413902	−	0.910321i	$-0.635835\pi$
$89$	−7.80950	−0.827805	−0.413902	+	0.910321i	$0.635835\pi$
$90$	5.87558	0.619340
$91$	0	0
$92$	17.8879	1.86495
$93$	1.11538	0.115660
$94$	22.9494	2.36705
$95$	−18.8743	−1.93646
$96$	2.54966	0.260224
$97$	−0.287042	−0.0291447	−0.0145723	−	0.999894i	$-0.504639\pi$
$97$	−0.287042	−0.0291447	−0.0145723	+	0.999894i	$0.504639\pi$
$98$	2.49813	0.252350
$99$	5.16537	0.519140
$100$	2.25536	0.225536
$101$	12.9536	1.28893	0.644467	−	0.764632i	$-0.277079\pi$
$101$	12.9536	1.28893	0.644467	+	0.764632i	$0.277079\pi$
$102$	−4.26078	−0.421880
$103$	−6.53676	−0.644086	−0.322043	−	0.946725i	$-0.604370\pi$
$103$	−6.53676	−0.644086	−0.322043	+	0.946725i	$0.604370\pi$
$104$	0	0
$105$	−2.35199	−0.229530
$106$	29.7919	2.89365
$107$	−3.73899	−0.361462	−0.180731	−	0.983533i	$-0.557846\pi$
$107$	−3.73899	−0.361462	−0.180731	+	0.983533i	$0.557846\pi$
$108$	4.24068	0.408059
$109$	−10.1278	−0.970066	−0.485033	−	0.874496i	$-0.661192\pi$
$109$	−10.1278	−0.970066	−0.485033	+	0.874496i	$0.661192\pi$
$110$	30.3496	2.89372
$111$	8.21263	0.779508
$112$	−5.50198	−0.519888
$113$	16.5267	1.55471	0.777353	−	0.629065i	$-0.216562\pi$
$113$	16.5267	1.55471	0.777353	+	0.629065i	$0.216562\pi$
$114$	−20.0471	−1.87758
$115$	9.92111	0.925148
$116$	−22.2225	−2.06331
$117$	0	0
$118$	−7.44450	−0.685322
$119$	1.70559	0.156351
$120$	13.1653	1.20182
$121$	15.6811	1.42555
$122$	−36.4811	−3.30285
$123$	−6.75466	−0.609047
$124$	4.72996	0.424763
$125$	−10.5091	−0.939958
$126$	−2.49813	−0.222551
$127$	13.8279	1.22703	0.613516	−	0.789682i	$-0.289755\pi$
$127$	13.8279	1.22703	0.613516	+	0.789682i	$0.289755\pi$
$128$	−16.6771	−1.47406
$129$	−0.965145	−0.0849762
$130$	0	0
$131$	9.92612	0.867249	0.433624	−	0.901094i	$-0.357234\pi$
$131$	9.92612	0.867249	0.433624	+	0.901094i	$0.357234\pi$
$132$	21.9047	1.90656
$133$	8.02484	0.695842
$134$	−33.8407	−2.92339
$135$	2.35199	0.202427
$136$	−9.54703	−0.818651
$137$	8.60954	0.735563	0.367781	−	0.929912i	$-0.380117\pi$
$137$	8.60954	0.735563	0.367781	+	0.929912i	$0.380117\pi$
$138$	10.5376	0.897019
$139$	−9.92269	−0.841631	−0.420816	−	0.907146i	$-0.638256\pi$
$139$	−9.92269	−0.841631	−0.420816	+	0.907146i	$0.638256\pi$
$140$	−9.97401	−0.842958
$141$	9.18662	0.773653
$142$	0.794896	0.0667062
$143$	0	0
$144$	5.50198	0.458498
$145$	−12.3252	−1.02355
$146$	−1.35576	−0.112203
$147$	1.00000	0.0824786
$148$	34.8271	2.86277
$149$	−0.253154	−0.0207392	−0.0103696	−	0.999946i	$-0.503301\pi$
$149$	−0.253154	−0.0207392	−0.0103696	+	0.999946i	$0.503301\pi$
$150$	1.32861	0.108481
$151$	−19.1942	−1.56200	−0.780999	−	0.624532i	$-0.785290\pi$
$151$	−19.1942	−1.56200	−0.780999	+	0.624532i	$0.785290\pi$
$152$	−44.9191	−3.64342
$153$	−1.70559	−0.137888
$154$	−12.9038	−1.03982
$155$	2.62336	0.210713
$156$	0	0
$157$	−14.8981	−1.18900	−0.594500	−	0.804096i	$-0.702650\pi$
$157$	−14.8981	−1.18900	−0.594500	+	0.804096i	$0.702650\pi$
$158$	−33.0505	−2.62935
$159$	11.9257	0.945768
$160$	5.99676	0.474086
$161$	−4.21818	−0.332439
$162$	2.49813	0.196272
$163$	−5.80688	−0.454830	−0.227415	−	0.973798i	$-0.573027\pi$
$163$	−5.80688	−0.454830	−0.227415	+	0.973798i	$0.573027\pi$
$164$	−28.6443	−2.23674
$165$	12.1489	0.945790
$166$	14.4716	1.12321
$167$	21.4231	1.65777	0.828885	−	0.559419i	$-0.188976\pi$
$167$	21.4231	1.65777	0.828885	+	0.559419i	$0.188976\pi$
$168$	−5.59751	−0.431857
$169$	0	0
$170$	−10.0213	−0.768599
$171$	−8.02484	−0.613675
$172$	−4.09286	−0.312078
$173$	21.4128	1.62798	0.813991	−	0.580878i	$-0.197290\pi$
$173$	21.4128	1.62798	0.813991	+	0.580878i	$0.197290\pi$
$174$	−13.0910	−0.992429
$175$	−0.531841	−0.0402034
$176$	28.4198	2.14222
$177$	−2.98003	−0.223992
$178$	−19.5092	−1.46227
$179$	5.04689	0.377222	0.188611	−	0.982052i	$-0.439601\pi$
$179$	5.04689	0.377222	0.188611	+	0.982052i	$0.439601\pi$
$180$	9.97401	0.743419
$181$	15.8878	1.18093	0.590464	−	0.807064i	$-0.298945\pi$
$181$	15.8878	1.18093	0.590464	+	0.807064i	$0.298945\pi$
$182$	0	0
$183$	−14.6034	−1.07951
$184$	23.6113	1.74065
$185$	19.3160	1.42014
$186$	2.78637	0.204306
$187$	−8.80999	−0.644250
$188$	38.9575	2.84127
$189$	−1.00000	−0.0727393
$190$	−47.1506	−3.42066
$191$	13.3753	0.967801	0.483901	−	0.875123i	$-0.339220\pi$
$191$	13.3753	0.967801	0.483901	+	0.875123i	$0.339220\pi$
$192$	−4.63456	−0.334471
$193$	−6.66748	−0.479935	−0.239968	−	0.970781i	$-0.577137\pi$
$193$	−6.66748	−0.479935	−0.239968	+	0.970781i	$0.577137\pi$
$194$	−0.717068	−0.0514825
$195$	0	0
$196$	4.24068	0.302905
$197$	12.3543	0.880210	0.440105	−	0.897946i	$-0.354941\pi$
$197$	12.3543	0.880210	0.440105	+	0.897946i	$0.354941\pi$
$198$	12.9038	0.917033
$199$	−14.5437	−1.03098	−0.515488	−	0.856897i	$-0.672389\pi$
$199$	−14.5437	−1.03098	−0.515488	+	0.856897i	$0.672389\pi$
$200$	2.97698	0.210505
$201$	−13.5464	−0.955489
$202$	32.3599	2.27683
$203$	5.24033	0.367799
$204$	−7.23283	−0.506400
$205$	−15.8869	−1.10959
$206$	−16.3297	−1.13774
$207$	4.21818	0.293184
$208$	0	0
$209$	−41.4513	−2.86725
$210$	−5.87558	−0.405453
$211$	25.6088	1.76298	0.881491	−	0.472200i	$-0.156540\pi$
$211$	25.6088	1.76298	0.881491	+	0.472200i	$0.156540\pi$
$212$	50.5729	3.47336
$213$	0.318196	0.0218024
$214$	−9.34050	−0.638503
$215$	−2.27001	−0.154813
$216$	5.59751	0.380862
$217$	−1.11538	−0.0757169
$218$	−25.3006	−1.71357
$219$	−0.542709	−0.0366729
$220$	51.5195	3.47344
$221$	0	0
$222$	20.5162	1.37696
$223$	8.99291	0.602210	0.301105	−	0.953591i	$-0.402645\pi$
$223$	8.99291	0.602210	0.301105	+	0.953591i	$0.402645\pi$
$224$	−2.54966	−0.170356
$225$	0.531841	0.0354561
$226$	41.2860	2.74631
$227$	4.16233	0.276263	0.138132	−	0.990414i	$-0.455890\pi$
$227$	4.16233	0.276263	0.138132	+	0.990414i	$0.455890\pi$
$228$	−34.0307	−2.25374
$229$	8.47202	0.559847	0.279924	−	0.960022i	$-0.409691\pi$
$229$	8.47202	0.559847	0.279924	+	0.960022i	$0.409691\pi$
$230$	24.7843	1.63423
$231$	−5.16537	−0.339857
$232$	−29.3328	−1.92579
$233$	−18.5357	−1.21432	−0.607158	−	0.794581i	$-0.707691\pi$
$233$	−18.5357	−1.21432	−0.607158	+	0.794581i	$0.707691\pi$
$234$	0	0
$235$	21.6068	1.40947
$236$	−12.6373	−0.822620
$237$	−13.2301	−0.859384
$238$	4.26078	0.276185
$239$	−0.176911	−0.0114434	−0.00572171	−	0.999984i	$-0.501821\pi$
$239$	−0.176911	−0.0114434	−0.00572171	+	0.999984i	$0.501821\pi$
$240$	12.9406	0.835310
$241$	−4.99572	−0.321803	−0.160901	−	0.986970i	$-0.551440\pi$
$241$	−4.99572	−0.321803	−0.160901	+	0.986970i	$0.551440\pi$
$242$	39.1735	2.51817
$243$	1.00000	0.0641500
$244$	−61.9281	−3.96454
$245$	2.35199	0.150263
$246$	−16.8740	−1.07585
$247$	0	0
$248$	6.24335	0.396453
$249$	5.79295	0.367113
$250$	−26.2530	−1.66039
$251$	0.560900	0.0354037	0.0177019	−	0.999843i	$-0.494365\pi$
$251$	0.560900	0.0354037	0.0177019	+	0.999843i	$0.494365\pi$
$252$	−4.24068	−0.267137
$253$	21.7885	1.36983
$254$	34.5441	2.16749
$255$	−4.01151	−0.251211
$256$	−32.3924	−2.02453
$257$	−16.9596	−1.05791	−0.528954	−	0.848650i	$-0.677416\pi$
$257$	−16.9596	−1.05791	−0.528954	+	0.848650i	$0.677416\pi$
$258$	−2.41106	−0.150106
$259$	−8.21263	−0.510308
$260$	0	0
$261$	−5.24033	−0.324368
$262$	24.7968	1.53195
$263$	7.29257	0.449679	0.224839	−	0.974396i	$-0.427814\pi$
$263$	7.29257	0.449679	0.224839	+	0.974396i	$0.427814\pi$
$264$	28.9132	1.77949
$265$	28.0490	1.72304
$266$	20.0471	1.22917
$267$	−7.80950	−0.477933
$268$	−57.4459	−3.50906
$269$	1.71166	0.104362	0.0521809	−	0.998638i	$-0.483383\pi$
$269$	1.71166	0.104362	0.0521809	+	0.998638i	$0.483383\pi$
$270$	5.87558	0.357576
$271$	−12.2573	−0.744575	−0.372288	−	0.928117i	$-0.621427\pi$
$271$	−12.2573	−0.744575	−0.372288	+	0.928117i	$0.621427\pi$
$272$	−9.38409	−0.568994
$273$	0	0
$274$	21.5078	1.29933
$275$	2.74716	0.165660
$276$	17.8879	1.07673
$277$	32.0290	1.92444	0.962218	−	0.272279i	$-0.0877775\pi$
$277$	32.0290	1.92444	0.962218	+	0.272279i	$0.0877775\pi$
$278$	−24.7882	−1.48670
$279$	1.11538	0.0667761
$280$	−13.1653	−0.786775
$281$	−25.3153	−1.51018	−0.755091	−	0.655620i	$-0.772408\pi$
$281$	−25.3153	−1.51018	−0.755091	+	0.655620i	$0.772408\pi$
$282$	22.9494	1.36662
$283$	−8.29593	−0.493142	−0.246571	−	0.969125i	$-0.579304\pi$
$283$	−8.29593	−0.493142	−0.246571	+	0.969125i	$0.579304\pi$
$284$	1.34937	0.0800701
$285$	−18.8743	−1.11802
$286$	0	0
$287$	6.75466	0.398715
$288$	2.54966	0.150240
$289$	−14.0910	−0.828881
$290$	−30.7900	−1.80805
$291$	−0.287042	−0.0168267
$292$	−2.30145	−0.134682
$293$	−26.9892	−1.57672	−0.788362	−	0.615211i	$-0.789071\pi$
$293$	−26.9892	−1.57672	−0.788362	+	0.615211i	$0.789071\pi$
$294$	2.49813	0.145694
$295$	−7.00898	−0.408079
$296$	45.9702	2.67197
$297$	5.16537	0.299725
$298$	−0.632414	−0.0366348
$299$	0	0
$300$	2.25536	0.130214
$301$	0.965145	0.0556300
$302$	−47.9496	−2.75919
$303$	12.9536	0.744166
$304$	−44.1525	−2.53232
$305$	−34.3469	−1.96670
$306$	−4.26078	−0.243573
$307$	−7.63819	−0.435935	−0.217967	−	0.975956i	$-0.569943\pi$
$307$	−7.63819	−0.435935	−0.217967	+	0.975956i	$0.569943\pi$
$308$	−21.9047	−1.24813
$309$	−6.53676	−0.371863
$310$	6.55350	0.372214
$311$	−3.99085	−0.226301	−0.113150	−	0.993578i	$-0.536094\pi$
$311$	−3.99085	−0.226301	−0.113150	+	0.993578i	$0.536094\pi$
$312$	0	0
$313$	11.1267	0.628920	0.314460	−	0.949271i	$-0.398177\pi$
$313$	11.1267	0.628920	0.314460	+	0.949271i	$0.398177\pi$
$314$	−37.2175	−2.10031
$315$	−2.35199	−0.132519
$316$	−56.1044	−3.15612
$317$	6.72186	0.377537	0.188769	−	0.982022i	$-0.439550\pi$
$317$	6.72186	0.377537	0.188769	+	0.982022i	$0.439550\pi$
$318$	29.7919	1.67065
$319$	−27.0682	−1.51553
$320$	−10.9004	−0.609352
$321$	−3.73899	−0.208690
$322$	−10.5376	−0.587237
$323$	13.6870	0.761567
$324$	4.24068	0.235593
$325$	0	0
$326$	−14.5064	−0.803434
$327$	−10.1278	−0.560068
$328$	−37.8092	−2.08767
$329$	−9.18662	−0.506475
$330$	30.3496	1.67069
$331$	−19.4811	−1.07078	−0.535390	−	0.844605i	$-0.679835\pi$
$331$	−19.4811	−1.07078	−0.535390	+	0.844605i	$0.679835\pi$
$332$	24.5660	1.34824
$333$	8.21263	0.450049
$334$	53.5178	2.92836
$335$	−31.8609	−1.74075
$336$	−5.50198	−0.300157
$337$	−6.57866	−0.358362	−0.179181	−	0.983816i	$-0.557345\pi$
$337$	−6.57866	−0.358362	−0.179181	+	0.983816i	$0.557345\pi$
$338$	0	0
$339$	16.5267	0.897609
$340$	−17.0115	−0.922580
$341$	5.76136	0.311995
$342$	−20.0471	−1.08402
$343$	−1.00000	−0.0539949
$344$	−5.40240	−0.291278
$345$	9.92111	0.534134
$346$	53.4920	2.87575
$347$	13.4028	0.719498	0.359749	−	0.933049i	$-0.382862\pi$
$347$	13.4028	0.719498	0.359749	+	0.933049i	$0.382862\pi$
$348$	−22.2225	−1.19125
$349$	−16.3285	−0.874045	−0.437022	−	0.899451i	$-0.643967\pi$
$349$	−16.3285	−0.874045	−0.437022	+	0.899451i	$0.643967\pi$
$350$	−1.32861	−0.0710172
$351$	0	0
$352$	13.1699	0.701960
$353$	−21.5374	−1.14632	−0.573161	−	0.819443i	$-0.694283\pi$
$353$	−21.5374	−1.14632	−0.573161	+	0.819443i	$0.694283\pi$
$354$	−7.44450	−0.395671
$355$	0.748392	0.0397205
$356$	−33.1175	−1.75523
$357$	1.70559	0.0902691
$358$	12.6078	0.666344
$359$	31.8829	1.68272	0.841358	−	0.540478i	$-0.181757\pi$
$359$	31.8829	1.68272	0.841358	+	0.540478i	$0.181757\pi$
$360$	13.1653	0.693870
$361$	45.3980	2.38937
$362$	39.6898	2.08605
$363$	15.6811	0.823044
$364$	0	0
$365$	−1.27644	−0.0668122
$366$	−36.4811	−1.90690
$367$	14.9500	0.780381	0.390191	−	0.920734i	$-0.372409\pi$
$367$	14.9500	0.780381	0.390191	+	0.920734i	$0.372409\pi$
$368$	23.2083	1.20982
$369$	−6.75466	−0.351633
$370$	48.2539	2.50860
$371$	−11.9257	−0.619150
$372$	4.72996	0.245237
$373$	1.74166	0.0901798	0.0450899	−	0.998983i	$-0.485643\pi$
$373$	1.74166	0.0901798	0.0450899	+	0.998983i	$0.485643\pi$
$374$	−22.0085	−1.13803
$375$	−10.5091	−0.542685
$376$	51.4222	2.65190
$377$	0	0
$378$	−2.49813	−0.128490
$379$	−35.4778	−1.82237	−0.911186	−	0.411995i	$-0.864832\pi$
$379$	−35.4778	−1.82237	−0.911186	+	0.411995i	$0.864832\pi$
$380$	−80.0398	−4.10596
$381$	13.8279	0.708427
$382$	33.4132	1.70957
$383$	−22.1971	−1.13422	−0.567109	−	0.823642i	$-0.691938\pi$
$383$	−22.1971	−1.13422	−0.567109	+	0.823642i	$0.691938\pi$
$384$	−16.6771	−0.851048
$385$	−12.1489	−0.619165
$386$	−16.6563	−0.847781
$387$	−0.965145	−0.0490611
$388$	−1.21725	−0.0617965
$389$	3.44035	0.174433	0.0872163	−	0.996189i	$-0.472203\pi$
$389$	3.44035	0.174433	0.0872163	+	0.996189i	$0.472203\pi$
$390$	0	0
$391$	−7.19447	−0.363840
$392$	5.59751	0.282717
$393$	9.92612	0.500706
$394$	30.8628	1.55484
$395$	−31.1169	−1.56566
$396$	21.9047	1.10075
$397$	−17.9477	−0.900767	−0.450384	−	0.892835i	$-0.648713\pi$
$397$	−17.9477	−0.900767	−0.450384	+	0.892835i	$0.648713\pi$
$398$	−36.3321	−1.82116
$399$	8.02484	0.401744
$400$	2.92618	0.146309
$401$	19.7564	0.986587	0.493293	−	0.869863i	$-0.335793\pi$
$401$	19.7564	0.986587	0.493293	+	0.869863i	$0.335793\pi$
$402$	−33.8407	−1.68782
$403$	0	0
$404$	54.9321	2.73297
$405$	2.35199	0.116871
$406$	13.0910	0.649697
$407$	42.4213	2.10275
$408$	−9.54703	−0.472648
$409$	−20.3407	−1.00578	−0.502891	−	0.864350i	$-0.667730\pi$
$409$	−20.3407	−1.00578	−0.502891	+	0.864350i	$0.667730\pi$
$410$	−39.6875	−1.96003
$411$	8.60954	0.424677
$412$	−27.7203	−1.36568
$413$	2.98003	0.146637
$414$	10.5376	0.517894
$415$	13.6249	0.668822
$416$	0	0
$417$	−9.92269	−0.485916
$418$	−103.551	−5.06484
$419$	14.0084	0.684356	0.342178	−	0.939635i	$-0.388835\pi$
$419$	14.0084	0.684356	0.342178	+	0.939635i	$0.388835\pi$
$420$	−9.97401	−0.486682
$421$	−5.93566	−0.289286	−0.144643	−	0.989484i	$-0.546203\pi$
$421$	−5.93566	−0.289286	−0.144643	+	0.989484i	$0.546203\pi$
$422$	63.9742	3.11422
$423$	9.18662	0.446669
$424$	66.7541	3.24186
$425$	−0.907100	−0.0440008
$426$	0.794896	0.0385128
$427$	14.6034	0.706706
$428$	−15.8558	−0.766421
$429$	0	0
$430$	−5.67078	−0.273469
$431$	−10.9820	−0.528982	−0.264491	−	0.964388i	$-0.585204\pi$
$431$	−10.9820	−0.528982	−0.264491	+	0.964388i	$0.585204\pi$
$432$	5.50198	0.264714
$433$	6.59353	0.316865	0.158432	−	0.987370i	$-0.449356\pi$
$433$	6.59353	0.316865	0.158432	+	0.987370i	$0.449356\pi$
$434$	−2.78637	−0.133750
$435$	−12.3252	−0.590947
$436$	−42.9487	−2.05687
$437$	−33.8502	−1.61928
$438$	−1.35576	−0.0647807
$439$	−4.55826	−0.217554	−0.108777	−	0.994066i	$-0.534693\pi$
$439$	−4.55826	−0.217554	−0.108777	+	0.994066i	$0.534693\pi$
$440$	68.0035	3.24194
$441$	1.00000	0.0476190
$442$	0	0
$443$	6.84511	0.325221	0.162610	−	0.986690i	$-0.448009\pi$
$443$	6.84511	0.325221	0.162610	+	0.986690i	$0.448009\pi$
$444$	34.8271	1.65282
$445$	−18.3678	−0.870719
$446$	22.4655	1.06377
$447$	−0.253154	−0.0119738
$448$	4.63456	0.218962
$449$	15.9302	0.751791	0.375896	−	0.926662i	$-0.377335\pi$
$449$	15.9302	0.751791	0.375896	+	0.926662i	$0.377335\pi$
$450$	1.32861	0.0626313
$451$	−34.8903	−1.64292
$452$	70.0845	3.29650
$453$	−19.1942	−0.901820
$454$	10.3981	0.488005
$455$	0	0
$456$	−44.9191	−2.10353
$457$	11.3437	0.530638	0.265319	−	0.964161i	$-0.414523\pi$
$457$	11.3437	0.530638	0.265319	+	0.964161i	$0.414523\pi$
$458$	21.1643	0.988941
$459$	−1.70559	−0.0796099
$460$	42.0722	1.96163
$461$	−37.9495	−1.76749	−0.883743	−	0.467973i	$-0.844984\pi$
$461$	−37.9495	−1.76749	−0.883743	+	0.467973i	$0.844984\pi$
$462$	−12.9038	−0.600339
$463$	33.4984	1.55680	0.778401	−	0.627767i	$-0.216031\pi$
$463$	33.4984	1.55680	0.778401	+	0.627767i	$0.216031\pi$
$464$	−28.8322	−1.33850
$465$	2.62336	0.121655
$466$	−46.3047	−2.14503
$467$	11.6371	0.538500	0.269250	−	0.963070i	$-0.413224\pi$
$467$	11.6371	0.538500	0.269250	+	0.963070i	$0.413224\pi$
$468$	0	0
$469$	13.5464	0.625514
$470$	53.9767	2.48976
$471$	−14.8981	−0.686469
$472$	−16.6807	−0.767792
$473$	−4.98533	−0.229226
$474$	−33.0505	−1.51806
$475$	−4.26794	−0.195826
$476$	7.23283	0.331516
$477$	11.9257	0.546039
$478$	−0.441948	−0.0202142
$479$	−26.2836	−1.20093	−0.600465	−	0.799651i	$-0.705018\pi$
$479$	−26.2836	−1.20093	−0.600465	+	0.799651i	$0.705018\pi$
$480$	5.99676	0.273714
$481$	0	0
$482$	−12.4800	−0.568448
$483$	−4.21818	−0.191934
$484$	66.4984	3.02266
$485$	−0.675118	−0.0306555
$486$	2.49813	0.113318
$487$	13.9247	0.630990	0.315495	−	0.948927i	$-0.397829\pi$
$487$	13.9247	0.630990	0.315495	+	0.948927i	$0.397829\pi$
$488$	−81.7424	−3.70030
$489$	−5.80688	−0.262596
$490$	5.87558	0.265432
$491$	−23.3848	−1.05534	−0.527670	−	0.849449i	$-0.676934\pi$
$491$	−23.3848	−1.05534	−0.527670	+	0.849449i	$0.676934\pi$
$492$	−28.6443	−1.29139
$493$	8.93782	0.402539
$494$	0	0
$495$	12.1489	0.546052
$496$	6.13679	0.275550
$497$	−0.318196	−0.0142730
$498$	14.4716	0.648487
$499$	4.20079	0.188053	0.0940266	−	0.995570i	$-0.470026\pi$
$499$	4.20079	0.188053	0.0940266	+	0.995570i	$0.470026\pi$
$500$	−44.5655	−1.99303
$501$	21.4231	0.957114
$502$	1.40120	0.0625388
$503$	5.60179	0.249772	0.124886	−	0.992171i	$-0.460144\pi$
$503$	5.60179	0.249772	0.124886	+	0.992171i	$0.460144\pi$
$504$	−5.59751	−0.249333
$505$	30.4668	1.35575
$506$	54.4306	2.41973
$507$	0	0
$508$	58.6398	2.60172
$509$	7.88662	0.349568	0.174784	−	0.984607i	$-0.444077\pi$
$509$	7.88662	0.349568	0.174784	+	0.984607i	$0.444077\pi$
$510$	−10.0213	−0.443751
$511$	0.542709	0.0240080
$512$	−47.5665	−2.10216
$513$	−8.02484	−0.354305
$514$	−42.3673	−1.86874
$515$	−15.3744	−0.677475
$516$	−4.09286	−0.180178
$517$	47.4523	2.08695
$518$	−20.5162	−0.901432
$519$	21.4128	0.939916
$520$	0	0
$521$	30.5215	1.33717	0.668585	−	0.743635i	$-0.266900\pi$
$521$	30.5215	1.33717	0.668585	+	0.743635i	$0.266900\pi$
$522$	−13.0910	−0.572979
$523$	26.1984	1.14557	0.572787	−	0.819704i	$-0.305862\pi$
$523$	26.1984	1.14557	0.572787	+	0.819704i	$0.305862\pi$
$524$	42.0934	1.83886
$525$	−0.531841	−0.0232114
$526$	18.2178	0.794334
$527$	−1.90238	−0.0828688
$528$	28.4198	1.23681
$529$	−5.20695	−0.226389
$530$	70.0703	3.04366
$531$	−2.98003	−0.129322
$532$	34.0307	1.47542
$533$	0	0
$534$	−19.5092	−0.844244
$535$	−8.79405	−0.380200
$536$	−75.8260	−3.27519
$537$	5.04689	0.217789
$538$	4.27596	0.184350
$539$	5.16537	0.222488
$540$	9.97401	0.429213
$541$	−6.76840	−0.290996	−0.145498	−	0.989359i	$-0.546478\pi$
$541$	−6.76840	−0.290996	−0.145498	+	0.989359i	$0.546478\pi$
$542$	−30.6203	−1.31525
$543$	15.8878	0.681810
$544$	−4.34866	−0.186447
$545$	−23.8204	−1.02035
$546$	0	0
$547$	−39.8930	−1.70570	−0.852851	−	0.522155i	$-0.825128\pi$
$547$	−39.8930	−1.70570	−0.852851	+	0.522155i	$0.825128\pi$
$548$	36.5103	1.55964
$549$	−14.6034	−0.623256
$550$	6.86277	0.292629
$551$	42.0528	1.79151
$552$	23.6113	1.00496
$553$	13.2301	0.562599
$554$	80.0128	3.39942
$555$	19.3160	0.819918
$556$	−42.0789	−1.78454
$557$	20.7410	0.878825	0.439412	−	0.898285i	$-0.355187\pi$
$557$	20.7410	0.878825	0.439412	+	0.898285i	$0.355187\pi$
$558$	2.78637	0.117956
$559$	0	0
$560$	−12.9406	−0.546839
$561$	−8.80999	−0.371958
$562$	−63.2410	−2.66766
$563$	46.2754	1.95027	0.975137	−	0.221602i	$-0.0711287\pi$
$563$	46.2754	1.95027	0.975137	+	0.221602i	$0.0711287\pi$
$564$	38.9575	1.64041
$565$	38.8707	1.63530
$566$	−20.7243	−0.871109
$567$	−1.00000	−0.0419961
$568$	1.78110	0.0747334
$569$	−13.9515	−0.584879	−0.292439	−	0.956284i	$-0.594467\pi$
$569$	−13.9515	−0.584879	−0.292439	+	0.956284i	$0.594467\pi$
$570$	−47.1506	−1.97492
$571$	25.4059	1.06320	0.531602	−	0.846994i	$-0.321590\pi$
$571$	25.4059	1.06320	0.531602	+	0.846994i	$0.321590\pi$
$572$	0	0
$573$	13.3753	0.558760
$574$	16.8740	0.704309
$575$	2.24340	0.0935563
$576$	−4.63456	−0.193107
$577$	−44.9472	−1.87118	−0.935588	−	0.353093i	$-0.885130\pi$
$577$	−44.9472	−1.87118	−0.935588	+	0.353093i	$0.885130\pi$
$578$	−35.2012	−1.46418
$579$	−6.66748	−0.277091
$580$	−52.2671	−2.17027
$581$	−5.79295	−0.240332
$582$	−0.717068	−0.0297234
$583$	61.6006	2.55124
$584$	−3.03782	−0.125706
$585$	0	0
$586$	−67.4226	−2.78520
$587$	23.2272	0.958688	0.479344	−	0.877627i	$-0.340875\pi$
$587$	23.2272	0.958688	0.479344	+	0.877627i	$0.340875\pi$
$588$	4.24068	0.174882
$589$	−8.95074	−0.368809
$590$	−17.5094	−0.720850
$591$	12.3543	0.508189
$592$	45.1857	1.85712
$593$	−9.16296	−0.376278	−0.188139	−	0.982142i	$-0.560245\pi$
$593$	−9.16296	−0.376278	−0.188139	+	0.982142i	$0.560245\pi$
$594$	12.9038	0.529449
$595$	4.01151	0.164456
$596$	−1.07355	−0.0439742
$597$	−14.5437	−0.595234
$598$	0	0
$599$	25.8168	1.05485	0.527424	−	0.849602i	$-0.323158\pi$
$599$	25.8168	1.05485	0.527424	+	0.849602i	$0.323158\pi$
$600$	2.97698	0.121535
$601$	17.8496	0.728102	0.364051	−	0.931379i	$-0.381393\pi$
$601$	17.8496	0.728102	0.364051	+	0.931379i	$0.381393\pi$
$602$	2.41106	0.0982675
$603$	−13.5464	−0.551652
$604$	−81.3962	−3.31196
$605$	36.8817	1.49946
$606$	32.3599	1.31453
$607$	34.2992	1.39216	0.696081	−	0.717963i	$-0.254925\pi$
$607$	34.2992	1.39216	0.696081	+	0.717963i	$0.254925\pi$
$608$	−20.4606	−0.829787
$609$	5.24033	0.212349
$610$	−85.8031	−3.47407
$611$	0	0
$612$	−7.23283	−0.292370
$613$	0.143589	0.00579952	0.00289976	−	0.999996i	$-0.499077\pi$
$613$	0.143589	0.00579952	0.00289976	+	0.999996i	$0.499077\pi$
$614$	−19.0812	−0.770056
$615$	−15.8869	−0.640620
$616$	−28.9132	−1.16495
$617$	−18.3135	−0.737272	−0.368636	−	0.929574i	$-0.620175\pi$
$617$	−18.3135	−0.737272	−0.368636	+	0.929574i	$0.620175\pi$
$618$	−16.3297	−0.656877
$619$	−0.301686	−0.0121258	−0.00606289	−	0.999982i	$-0.501930\pi$
$619$	−0.301686	−0.0121258	−0.00606289	+	0.999982i	$0.501930\pi$
$620$	11.1248	0.446783
$621$	4.21818	0.169270
$622$	−9.96969	−0.399748
$623$	7.80950	0.312881
$624$	0	0
$625$	−27.3764	−1.09505
$626$	27.7961	1.11095
$627$	−41.4513	−1.65540
$628$	−63.1781	−2.52108
$629$	−14.0073	−0.558509
$630$	−5.87558	−0.234089
$631$	20.3829	0.811432	0.405716	−	0.913999i	$-0.367022\pi$
$631$	20.3829	0.811432	0.405716	+	0.913999i	$0.367022\pi$
$632$	−74.0553	−2.94576
$633$	25.6088	1.01786
$634$	16.7921	0.666900
$635$	32.5231	1.29064
$636$	50.5729	2.00535
$637$	0	0
$638$	−67.6201	−2.67711
$639$	0.318196	0.0125876
$640$	−39.2243	−1.55047
$641$	20.7666	0.820233	0.410116	−	0.912033i	$-0.365488\pi$
$641$	20.7666	0.820233	0.410116	+	0.912033i	$0.365488\pi$
$642$	−9.34050	−0.368640
$643$	−11.0348	−0.435171	−0.217585	−	0.976041i	$-0.569818\pi$
$643$	−11.0348	−0.435171	−0.217585	+	0.976041i	$0.569818\pi$
$644$	−17.8879	−0.704883
$645$	−2.27001	−0.0893814
$646$	34.1921	1.34527
$647$	−37.5007	−1.47430	−0.737152	−	0.675727i	$-0.763830\pi$
$647$	−37.5007	−1.47430	−0.737152	+	0.675727i	$0.763830\pi$
$648$	5.59751	0.219891
$649$	−15.3929	−0.604226
$650$	0	0
$651$	−1.11538	−0.0437152
$652$	−24.6251	−0.964394
$653$	−26.8688	−1.05146	−0.525729	−	0.850652i	$-0.676207\pi$
$653$	−26.8688	−1.05146	−0.525729	+	0.850652i	$0.676207\pi$
$654$	−25.3006	−0.989331
$655$	23.3461	0.912207
$656$	−37.1640	−1.45101
$657$	−0.542709	−0.0211731
$658$	−22.9494	−0.894662
$659$	10.8847	0.424008	0.212004	−	0.977269i	$-0.432001\pi$
$659$	10.8847	0.424008	0.212004	+	0.977269i	$0.432001\pi$
$660$	51.5195	2.00539
$661$	−10.7257	−0.417181	−0.208590	−	0.978003i	$-0.566888\pi$
$661$	−10.7257	−0.417181	−0.208590	+	0.978003i	$0.566888\pi$
$662$	−48.6665	−1.89148
$663$	0	0
$664$	32.4261	1.25838
$665$	18.8743	0.731914
$666$	20.5162	0.794988
$667$	−22.1046	−0.855895
$668$	90.8485	3.51503
$669$	8.99291	0.347686
$670$	−79.5929	−3.07494
$671$	−75.4318	−2.91201
$672$	−2.54966	−0.0983552
$673$	−22.2093	−0.856104	−0.428052	−	0.903754i	$-0.640800\pi$
$673$	−22.2093	−0.856104	−0.428052	+	0.903754i	$0.640800\pi$
$674$	−16.4344	−0.633028
$675$	0.531841	0.0204706
$676$	0	0
$677$	3.83321	0.147322	0.0736612	−	0.997283i	$-0.476532\pi$
$677$	3.83321	0.147322	0.0736612	+	0.997283i	$0.476532\pi$
$678$	41.2860	1.58558
$679$	0.287042	0.0110156
$680$	−22.4545	−0.861090
$681$	4.16233	0.159501
$682$	14.3926	0.551123
$683$	6.80946	0.260557	0.130278	−	0.991477i	$-0.458413\pi$
$683$	6.80946	0.260557	0.130278	+	0.991477i	$0.458413\pi$
$684$	−34.0307	−1.30120
$685$	20.2495	0.773695
$686$	−2.49813	−0.0953792
$687$	8.47202	0.323228
$688$	−5.31020	−0.202450
$689$	0	0
$690$	24.7843	0.943520
$691$	1.14161	0.0434288	0.0217144	−	0.999764i	$-0.493088\pi$
$691$	1.14161	0.0434288	0.0217144	+	0.999764i	$0.493088\pi$
$692$	90.8046	3.45187
$693$	−5.16537	−0.196216
$694$	33.4819	1.27096
$695$	−23.3380	−0.885262
$696$	−29.3328	−1.11186
$697$	11.5206	0.436375
$698$	−40.7908	−1.54395
$699$	−18.5357	−0.701086
$700$	−2.25536	−0.0852448
$701$	8.44188	0.318845	0.159423	−	0.987210i	$-0.449037\pi$
$701$	8.44188	0.318845	0.159423	+	0.987210i	$0.449037\pi$
$702$	0	0
$703$	−65.9050	−2.48565
$704$	−23.9392	−0.902244
$705$	21.6068	0.813760
$706$	−53.8034	−2.02492
$707$	−12.9536	−0.487171
$708$	−12.6373	−0.474940
$709$	−7.11295	−0.267133	−0.133566	−	0.991040i	$-0.542643\pi$
$709$	−7.11295	−0.267133	−0.133566	+	0.991040i	$0.542643\pi$
$710$	1.86958	0.0701643
$711$	−13.2301	−0.496166
$712$	−43.7137	−1.63824
$713$	4.70487	0.176199
$714$	4.26078	0.159456
$715$	0	0
$716$	21.4022	0.799839
$717$	−0.176911	−0.00660687
$718$	79.6478	2.97243
$719$	6.74382	0.251502	0.125751	−	0.992062i	$-0.459866\pi$
$719$	6.74382	0.251502	0.125751	+	0.992062i	$0.459866\pi$
$720$	12.9406	0.482267
$721$	6.53676	0.243442
$722$	113.410	4.22069
$723$	−4.99572	−0.185793
$724$	67.3749	2.50397
$725$	−2.78702	−0.103507
$726$	39.1735	1.45386
$727$	−23.9650	−0.888811	−0.444406	−	0.895826i	$-0.646585\pi$
$727$	−23.9650	−0.888811	−0.444406	+	0.895826i	$0.646585\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.18873	−0.118020
$731$	1.64614	0.0608846
$732$	−61.9281	−2.28893
$733$	5.63526	0.208143	0.104072	−	0.994570i	$-0.466813\pi$
$733$	5.63526	0.208143	0.104072	+	0.994570i	$0.466813\pi$
$734$	37.3470	1.37850
$735$	2.35199	0.0867543
$736$	10.7549	0.396432
$737$	−69.9722	−2.57746
$738$	−16.8740	−0.621142
$739$	18.7986	0.691518	0.345759	−	0.938323i	$-0.387622\pi$
$739$	18.7986	0.691518	0.345759	+	0.938323i	$0.387622\pi$
$740$	81.9128	3.01118
$741$	0	0
$742$	−29.7919	−1.09370
$743$	27.2365	0.999209	0.499604	−	0.866254i	$-0.333479\pi$
$743$	27.2365	0.999209	0.499604	+	0.866254i	$0.333479\pi$
$744$	6.24335	0.228892
$745$	−0.595416	−0.0218144
$746$	4.35090	0.159298
$747$	5.79295	0.211953
$748$	−37.3603	−1.36603
$749$	3.73899	0.136620
$750$	−26.2530	−0.958625
$751$	17.2816	0.630615	0.315308	−	0.948989i	$-0.397892\pi$
$751$	17.2816	0.630615	0.315308	+	0.948989i	$0.397892\pi$
$752$	50.5446	1.84317
$753$	0.560900	0.0204403
$754$	0	0
$755$	−45.1444	−1.64297
$756$	−4.24068	−0.154232
$757$	−10.1844	−0.370160	−0.185080	−	0.982723i	$-0.559254\pi$
$757$	−10.1844	−0.370160	−0.185080	+	0.982723i	$0.559254\pi$
$758$	−88.6283	−3.21913
$759$	21.7885	0.790872
$760$	−105.649	−3.83230
$761$	51.1035	1.85250	0.926251	−	0.376908i	$-0.123013\pi$
$761$	51.1035	1.85250	0.926251	+	0.376908i	$0.123013\pi$
$762$	34.5441	1.25140
$763$	10.1278	0.366651
$764$	56.7202	2.05206
$765$	−4.01151	−0.145037
$766$	−55.4513	−2.00354
$767$	0	0
$768$	−32.3924	−1.16886
$769$	26.3949	0.951823	0.475911	−	0.879493i	$-0.342118\pi$
$769$	26.3949	0.951823	0.475911	+	0.879493i	$0.342118\pi$
$770$	−30.3496	−1.09372
$771$	−16.9596	−0.610784
$772$	−28.2746	−1.01763
$773$	−10.1413	−0.364758	−0.182379	−	0.983228i	$-0.558380\pi$
$773$	−10.1413	−0.364758	−0.182379	+	0.983228i	$0.558380\pi$
$774$	−2.41106	−0.0866638
$775$	0.593205	0.0213085
$776$	−1.60672	−0.0576778
$777$	−8.21263	−0.294626
$778$	8.59445	0.308126
$779$	54.2050	1.94210
$780$	0	0
$781$	1.64360	0.0588127
$782$	−17.9727	−0.642704
$783$	−5.24033	−0.187274
$784$	5.50198	0.196499
$785$	−35.0402	−1.25064
$786$	24.7968	0.884472
$787$	51.5981	1.83927	0.919636	−	0.392771i	$-0.128484\pi$
$787$	51.5981	1.83927	0.919636	+	0.392771i	$0.128484\pi$
$788$	52.3907	1.86634
$789$	7.29257	0.259622
$790$	−77.7342	−2.76566
$791$	−16.5267	−0.587623
$792$	28.9132	1.02739
$793$	0	0
$794$	−44.8357	−1.59116
$795$	28.0490	0.994797
$796$	−61.6751	−2.18602
$797$	−15.1299	−0.535928	−0.267964	−	0.963429i	$-0.586351\pi$
$797$	−15.1299	−0.535928	−0.267964	+	0.963429i	$0.586351\pi$
$798$	20.0471	0.709660
$799$	−15.6686	−0.554314
$800$	1.35601	0.0479423
$801$	−7.80950	−0.275935
$802$	49.3541	1.74275
$803$	−2.80330	−0.0989261
$804$	−57.4459	−2.02596
$805$	−9.92111	−0.349673
$806$	0	0
$807$	1.71166	0.0602533
$808$	72.5080	2.55082
$809$	4.43586	0.155956	0.0779782	−	0.996955i	$-0.475154\pi$
$809$	4.43586	0.155956	0.0779782	+	0.996955i	$0.475154\pi$
$810$	5.87558	0.206447
$811$	−3.05676	−0.107337	−0.0536686	−	0.998559i	$-0.517091\pi$
$811$	−3.05676	−0.107337	−0.0536686	+	0.998559i	$0.517091\pi$
$812$	22.2225	0.779858
$813$	−12.2573	−0.429881
$814$	105.974	3.71439
$815$	−13.6577	−0.478409
$816$	−9.38409	−0.328509
$817$	7.74513	0.270968
$818$	−50.8138	−1.77666
$819$	0	0
$820$	−67.3710	−2.35270
$821$	11.0373	0.385204	0.192602	−	0.981277i	$-0.438307\pi$
$821$	11.0373	0.385204	0.192602	+	0.981277i	$0.438307\pi$
$822$	21.5078	0.750170
$823$	49.7386	1.73378	0.866890	−	0.498499i	$-0.166115\pi$
$823$	49.7386	1.73378	0.866890	+	0.498499i	$0.166115\pi$
$824$	−36.5895	−1.27466
$825$	2.74716	0.0956438
$826$	7.44450	0.259027
$827$	42.7670	1.48715	0.743577	−	0.668650i	$-0.233128\pi$
$827$	42.7670	1.48715	0.743577	+	0.668650i	$0.233128\pi$
$828$	17.8879	0.621649
$829$	−11.5052	−0.399591	−0.199796	−	0.979838i	$-0.564028\pi$
$829$	−11.5052	−0.399591	−0.199796	+	0.979838i	$0.564028\pi$
$830$	34.0369	1.18144
$831$	32.0290	1.11107
$832$	0	0
$833$	−1.70559	−0.0590950
$834$	−24.7882	−0.858345
$835$	50.3869	1.74371
$836$	−175.781	−6.07953
$837$	1.11538	0.0385532
$838$	34.9949	1.20888
$839$	−10.5561	−0.364436	−0.182218	−	0.983258i	$-0.558328\pi$
$839$	−10.5561	−0.364436	−0.182218	+	0.983258i	$0.558328\pi$
$840$	−13.1653	−0.454245
$841$	−1.53898	−0.0530681
$842$	−14.8281	−0.511009
$843$	−25.3153	−0.871904
$844$	108.599	3.73812
$845$	0	0
$846$	22.9494	0.789017
$847$	−15.6811	−0.538809
$848$	65.6148	2.25322
$849$	−8.29593	−0.284715
$850$	−2.26606	−0.0777251
$851$	34.6423	1.18752
$852$	1.34937	0.0462285
$853$	−2.34131	−0.0801648	−0.0400824	−	0.999196i	$-0.512762\pi$
$853$	−2.34131	−0.0801648	−0.0400824	+	0.999196i	$0.512762\pi$
$854$	36.4811	1.24836
$855$	−18.8743	−0.645488
$856$	−20.9290	−0.715339
$857$	−47.5469	−1.62417	−0.812086	−	0.583537i	$-0.801668\pi$
$857$	−47.5469	−1.62417	−0.812086	+	0.583537i	$0.801668\pi$
$858$	0	0
$859$	49.5483	1.69057	0.845284	−	0.534318i	$-0.179431\pi$
$859$	49.5483	1.69057	0.845284	+	0.534318i	$0.179431\pi$
$860$	−9.62636	−0.328256
$861$	6.75466	0.230198
$862$	−27.4344	−0.934419
$863$	0.233810	0.00795899	0.00397949	−	0.999992i	$-0.498733\pi$
$863$	0.233810	0.00795899	0.00397949	+	0.999992i	$0.498733\pi$
$864$	2.54966	0.0867412
$865$	50.3625	1.71238
$866$	16.4715	0.559725
$867$	−14.0910	−0.478555
$868$	−4.72996	−0.160545
$869$	−68.3382	−2.31821
$870$	−30.7900	−1.04388
$871$	0	0
$872$	−56.6904	−1.91978
$873$	−0.287042	−0.00971489
$874$	−84.5624	−2.86037
$875$	10.5091	0.355271
$876$	−2.30145	−0.0777589
$877$	21.2880	0.718845	0.359423	−	0.933175i	$-0.382974\pi$
$877$	21.2880	0.718845	0.359423	+	0.933175i	$0.382974\pi$
$878$	−11.3872	−0.384298
$879$	−26.9892	−0.910322
$880$	66.8429	2.25327
$881$	17.0535	0.574546	0.287273	−	0.957849i	$-0.407251\pi$
$881$	17.0535	0.574546	0.287273	+	0.957849i	$0.407251\pi$
$882$	2.49813	0.0841166
$883$	15.7586	0.530319	0.265160	−	0.964205i	$-0.414575\pi$
$883$	15.7586	0.530319	0.265160	+	0.964205i	$0.414575\pi$
$884$	0	0
$885$	−7.00898	−0.235604
$886$	17.1000	0.574486
$887$	−19.6096	−0.658425	−0.329212	−	0.944256i	$-0.606783\pi$
$887$	−19.6096	−0.658425	−0.329212	+	0.944256i	$0.606783\pi$
$888$	45.9702	1.54266
$889$	−13.8279	−0.463774
$890$	−45.8853	−1.53808
$891$	5.16537	0.173047
$892$	38.1360	1.27689
$893$	−73.7212	−2.46698
$894$	−0.632414	−0.0211511
$895$	11.8702	0.396778
$896$	16.6771	0.557142
$897$	0	0
$898$	39.7957	1.32800
$899$	−5.84496	−0.194940
$900$	2.25536	0.0751788
$901$	−20.3403	−0.677632
$902$	−87.1607	−2.90214
$903$	0.965145	0.0321180
$904$	92.5086	3.07679
$905$	37.3678	1.24215
$906$	−47.9496	−1.59302
$907$	8.16378	0.271074	0.135537	−	0.990772i	$-0.456724\pi$
$907$	8.16378	0.271074	0.135537	+	0.990772i	$0.456724\pi$
$908$	17.6511	0.585772
$909$	12.9536	0.429645
$910$	0	0
$911$	40.0348	1.32641	0.663206	−	0.748437i	$-0.269195\pi$
$911$	40.0348	1.32641	0.663206	+	0.748437i	$0.269195\pi$
$912$	−44.1525	−1.46203
$913$	29.9228	0.990299
$914$	28.3382	0.937345
$915$	−34.3469	−1.13547
$916$	35.9271	1.18706
$917$	−9.92612	−0.327789
$918$	−4.26078	−0.140627
$919$	−34.0730	−1.12396	−0.561982	−	0.827149i	$-0.689961\pi$
$919$	−34.0730	−1.12396	−0.561982	+	0.827149i	$0.689961\pi$
$920$	55.5335	1.83088
$921$	−7.63819	−0.251687
$922$	−94.8030	−3.12217
$923$	0	0
$924$	−21.9047	−0.720611
$925$	4.36781	0.143613
$926$	83.6835	2.75001
$927$	−6.53676	−0.214695
$928$	−13.3610	−0.438598
$929$	−20.8776	−0.684972	−0.342486	−	0.939523i	$-0.611269\pi$
$929$	−20.8776	−0.684972	−0.342486	+	0.939523i	$0.611269\pi$
$930$	6.55350	0.214898
$931$	−8.02484	−0.263003
$932$	−78.6040	−2.57476
$933$	−3.99085	−0.130655
$934$	29.0710	0.951232
$935$	−20.7210	−0.677648
$936$	0	0
$937$	20.5927	0.672734	0.336367	−	0.941731i	$-0.390802\pi$
$937$	20.5927	0.672734	0.336367	+	0.941731i	$0.390802\pi$
$938$	33.8407	1.10494
$939$	11.1267	0.363107
$940$	91.6275	2.98856
$941$	18.7149	0.610089	0.305045	−	0.952338i	$-0.401329\pi$
$941$	18.7149	0.610089	0.305045	+	0.952338i	$0.401329\pi$
$942$	−37.2175	−1.21261
$943$	−28.4924	−0.927839
$944$	−16.3960	−0.533645
$945$	−2.35199	−0.0765101
$946$	−12.4540	−0.404915
$947$	−5.23110	−0.169988	−0.0849939	−	0.996381i	$-0.527087\pi$
$947$	−5.23110	−0.169988	−0.0849939	+	0.996381i	$0.527087\pi$
$948$	−56.1044	−1.82218
$949$	0	0
$950$	−10.6619	−0.345917
$951$	6.72186	0.217971
$952$	9.54703	0.309421
$953$	−49.7229	−1.61068	−0.805341	−	0.592812i	$-0.798018\pi$
$953$	−49.7229	−1.61068	−0.805341	+	0.592812i	$0.798018\pi$
$954$	29.7919	0.964550
$955$	31.4585	1.01797
$956$	−0.750222	−0.0242639
$957$	−27.0682	−0.874992
$958$	−65.6601	−2.12138
$959$	−8.60954	−0.278017
$960$	−10.9004	−0.351810
$961$	−29.7559	−0.959869
$962$	0	0
$963$	−3.73899	−0.120487
$964$	−21.1852	−0.682330
$965$	−15.6818	−0.504815
$966$	−10.5376	−0.339041
$967$	−4.55490	−0.146476	−0.0732379	−	0.997314i	$-0.523333\pi$
$967$	−4.55490	−0.146476	−0.0732379	+	0.997314i	$0.523333\pi$
$968$	87.7750	2.82120
$969$	13.6870	0.439691
$970$	−1.68654	−0.0541514
$971$	33.4767	1.07432	0.537159	−	0.843481i	$-0.319497\pi$
$971$	33.4767	1.07432	0.537159	+	0.843481i	$0.319497\pi$
$972$	4.24068	0.136020
$973$	9.92269	0.318107
$974$	34.7859	1.11461
$975$	0	0
$976$	−80.3473	−2.57185
$977$	−48.7454	−1.55950	−0.779752	−	0.626089i	$-0.784655\pi$
$977$	−48.7454	−1.55950	−0.779752	+	0.626089i	$0.784655\pi$
$978$	−14.5064	−0.463863
$979$	−40.3390	−1.28924
$980$	9.97401	0.318608
$981$	−10.1278	−0.323355
$982$	−58.4183	−1.86420
$983$	5.57582	0.177841	0.0889205	−	0.996039i	$-0.471658\pi$
$983$	5.57582	0.177841	0.0889205	+	0.996039i	$0.471658\pi$
$984$	−37.8092	−1.20531
$985$	29.0572	0.925840
$986$	22.3279	0.711065
$987$	−9.18662	−0.292413
$988$	0	0
$989$	−4.07115	−0.129455
$990$	30.3496	0.964572
$991$	39.8543	1.26601	0.633006	−	0.774147i	$-0.281821\pi$
$991$	39.8543	1.26601	0.633006	+	0.774147i	$0.281821\pi$
$992$	2.84384	0.0902920
$993$	−19.4811	−0.618216
$994$	−0.794896	−0.0252126
$995$	−34.2066	−1.08442
$996$	24.5660	0.778404
$997$	−39.1045	−1.23845	−0.619226	−	0.785213i	$-0.712554\pi$
$997$	−39.1045	−1.23845	−0.619226	+	0.785213i	$0.712554\pi$
$998$	10.4941	0.332186
$999$	8.21263	0.259836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bh.1.13	yes	15
13.12	even	2		3549.2.a.bg.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.3	✓	15	13.12	even	2
3549.2.a.bh.1.13	yes	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+2.49813 q^{2} +1.00000 q^{3} +4.24068 q^{4} +2.35199 q^{5} +2.49813 q^{6} -1.00000 q^{7} +5.59751 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.49813 q^{2} +1.00000 q^{3} +4.24068 q^{4} +2.35199 q^{5} +2.49813 q^{6} -1.00000 q^{7} +5.59751 q^{8} +1.00000 q^{9} +5.87558 q^{10} +5.16537 q^{11} +4.24068 q^{12} -2.49813 q^{14} +2.35199 q^{15} +5.50198 q^{16} -1.70559 q^{17} +2.49813 q^{18} -8.02484 q^{19} +9.97401 q^{20} -1.00000 q^{21} +12.9038 q^{22} +4.21818 q^{23} +5.59751 q^{24} +0.531841 q^{25} +1.00000 q^{27} -4.24068 q^{28} -5.24033 q^{29} +5.87558 q^{30} +1.11538 q^{31} +2.54966 q^{32} +5.16537 q^{33} -4.26078 q^{34} -2.35199 q^{35} +4.24068 q^{36} +8.21263 q^{37} -20.0471 q^{38} +13.1653 q^{40} -6.75466 q^{41} -2.49813 q^{42} -0.965145 q^{43} +21.9047 q^{44} +2.35199 q^{45} +10.5376 q^{46} +9.18662 q^{47} +5.50198 q^{48} +1.00000 q^{49} +1.32861 q^{50} -1.70559 q^{51} +11.9257 q^{53} +2.49813 q^{54} +12.1489 q^{55} -5.59751 q^{56} -8.02484 q^{57} -13.0910 q^{58} -2.98003 q^{59} +9.97401 q^{60} -14.6034 q^{61} +2.78637 q^{62} -1.00000 q^{63} -4.63456 q^{64} +12.9038 q^{66} -13.5464 q^{67} -7.23283 q^{68} +4.21818 q^{69} -5.87558 q^{70} +0.318196 q^{71} +5.59751 q^{72} -0.542709 q^{73} +20.5162 q^{74} +0.531841 q^{75} -34.0307 q^{76} -5.16537 q^{77} -13.2301 q^{79} +12.9406 q^{80} +1.00000 q^{81} -16.8740 q^{82} +5.79295 q^{83} -4.24068 q^{84} -4.01151 q^{85} -2.41106 q^{86} -5.24033 q^{87} +28.9132 q^{88} -7.80950 q^{89} +5.87558 q^{90} +17.8879 q^{92} +1.11538 q^{93} +22.9494 q^{94} -18.8743 q^{95} +2.54966 q^{96} -0.287042 q^{97} +2.49813 q^{98} +5.16537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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